Bank of America and federal prosecutors have accelerated their negotiations to resolve an investigation into the bank’s sale of troubled mortgage securities before the financial crisis. The two sides, however, remain far apart on crucial issues and a settlement remained elusive late Wednesday, even after the bank significantly raised its offer.

The bank’s lawyers and Justice Department prosecutors met in Washington on Wednesday to discuss the size of a potential cash penalty, a major sticking point in the settlement talks, according to people briefed on the meeting. Heading into the meeting, the Justice Department was demanding roughly $17 billion to settle the case, more than $10 billion in the form of a cash penalty and the rest in so-called soft dollar payments to help struggling homeowners.

The bank was offering a total of $13 billion, the people said, including $4 billion in cash. The bank narrowed the gap on Wednesday, the people said, raising its cash offer to about $7 billion and its total proposal to roughly $14 billion.